Page "Church–Turing thesis" Paragraph 43

An attempt to understand the notion of " effective computability " better led Robin Gandy ( Turing's student and friend ) in 1980 to analyze machine computation ( as opposed to human-computation acted out by a Turing machine ).

Gandy's curiosity about, and analysis of, " cellular automata ", " Conway's game of life ", " parallelism " and " crystalline automata " led him to propose four " principles ( or constraints ) ... which it is argued, any machine must satisfy.

" His most-important fourth, " the principle of causality " is based on the " finite velocity of propagation of effects and signals ; contemporary physics rejects the possibility of instantaneous action at a distance.

" From these principles and some additional constraints —( 1a ) a lower bound on the linear dimensions of any of the parts, ( 1b ) an upper bound on speed of propagation ( the velocity of light ), ( 2 ) discrete progress of the machine, and ( 3 ) deterministic behavior — he produces a theorem that " What can be calculated by a device satisfying principles I – IV is computable.

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